Answer
$x = 3$
Work Step by Step
According to Theorem 6-15, the diagonals of a rectangle are congruent. Therefore, we can set $LN$ and $MP$, the diagonals of $LMNP$, equal to one another to solve for $x$:
$LN = MP$
Substitute with the expressions given for each diagonal:
$5x - 8 = 2x + 1$
Subtract $2x$ from each side of the equation to move variables to the left side of the equation:
$3x - 8 = 1$
Add $8$ to each side of the equation to move constants to the right side of the equation:
$3x = 9$
Divide each side by $3$ to solve for $x$:
$x = 3$
